Personalized optimal decision making, finding the optimal decision rule (ODR) based on individual characteristics, has attracted increasing attention recently in many fields, such as education, economics, and medicine. Current ODR methods usually require the primary outcome of interest in samples for assessing treatment effects, namely, the experimental sample. However, in many studies, treatments may have a long-term effect, and as such, the primary outcome of interest cannot be observed in the experimental sample due to the limited duration of experiments, which makes the estimation of ODR impossible. This paper is inspired to address this challenge by making use of an auxiliary sample to facilitate the estimation of ODR in the experimental sample. We propose an auGmented inverse propensity weighted Experimental and Auxiliary sample-based decision Rule (GEAR) by maximizing the augmented inverse propensity weighted value estimator over a class of decision rules using the experimental sample, with the primary outcome being imputed based on the auxiliary sample. The asymptotic properties of the proposed GEAR estimators and their associated value estimators are established. Simulation studies are conducted to demonstrate its empirical validity with a real AIDS application.

中文翻译：

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GEAR：关于辅助数据的最优决策

个性化最优决策，即根据个体特征寻找最优决策规则（ODR），近年来在教育、经济、医学等诸多领域受到越来越多的关注。当前的 ODR 方法通常需要对样本感兴趣的主要结果来评估治疗效果，即实验样本。然而，在许多研究中，治疗可能会产生长期影响，因此，由于实验持续时间有限，无法在实验样本中观察到感兴趣的主要结果，这使得 ODR 的估计变得不可能。本文旨在通过使用辅助样本来促进对实验样本中 ODR 的估计来解决这一挑战。我们通过使用实验样本最大化一类决策规则上的增强逆倾向加权值估计量，提出了一种增强逆倾向加权实验和辅助样本决策规则（GEAR），主要结果是基于辅助样本估算的。建立了所提出的 GEAR 估计器及其相关值估计器的渐近特性。进行模拟研究以证明其在实际 AIDS 应用中的实证有效性。建立了所提出的 GEAR 估计器及其相关值估计器的渐近特性。进行模拟研究以证明其在实际 AIDS 应用中的实证有效性。建立了所提出的 GEAR 估计器及其相关值估计器的渐近特性。进行模拟研究以证明其在实际 AIDS 应用中的实证有效性。